Every craft requires the right tools. You'll sew easier, faster and better with the necessary tools. Beyond that, there are other tools that simply make any crafting project easier.
Fiskars Scissor 8" Left HandScissors: Lousy scissors are hard to cut with, hack up your fabric and make your hand hurt. There are dozens of options to choose from and no one right pair of scissors. For starters, you need one pair of sharp, strong, smooth blade scissors. I primarily use Fiskars lefty scissors - they also come in a right hand model. I also have a pair of Ginger featherweight scissors for lightweight and delicate fabrics. Never cut paper, tape or hot dog wrappers with your sewing scissors. They dull faster and pick up substances that stain and corrode the blades and leave gunk on your fabric.
Seam ripper: I have a handful of seam rippers because the gremlins around here like to hide them, break them or turn them into action figure weapons. They make fancy seam rippers, ergonomic seam rippers and seam rippers for larger hands. Get what tickles your fancy, but be sure to have one close.
Straight pins: You need good dressmaker pins... throw away the short ones you get when you buy fabric at Walmart or a packaged dress shirt. Throw away the bent pins, the nicked and rusted pins. You don't strictly need a pincushion but they're cheap and handy. Some have an attached strawberry of slightly abrasive material to clean pins and needles. I also like a wrist pin cushion so the pins are always close.
Measuring tape: You need at least one good measuring tape.
Chalk: You can buy fancy chalks or use ordinary chalkboard chalk.
Sewing Machine: I'll write more about finding and buying a sewing machine later. For now, I am assuming you have access to one. Read the manual - really!